Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes
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- Belopolskaya, Y. & Woyczynski, W.A. Acta Appl Math (2007) 96: 55. doi:10.1007/s10440-007-9095-0
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We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE.